The problem is if you forget the fake details you can't recover the account. I was born around 1900 for my old yahoo groups email, but I forgot when exactly and so I got emails for a group I no longer cared about until (not sure what died, yahoo groups or the list)
I didn't hear of a password manager for another decade. Even if I had I'm now depending on it evisting (as opposed to lost in a disc crash or something)
If I think the fake details will be used for account recovery, and I actually care about the account, I store them in my password manager. (custom fields or notes in Bitearden).